We present a search for β⁺/EC double beta decay of ¹²⁰Te performed with the CUORICINO experiment, an array of TeO₂ cryogenic bolometers. After collecting 0.0573 kg·y of ¹²⁰Te, we see no evidence of a signal and therefore set the following limits on the half-life: T^0ν_1/2 > 1.9 × 10²¹ yr at 90% C.L. for the 0ν mode and T^2ν_1/2 > 7.6 × 10¹⁹ yr at 90% C.L. for the 2ν mode. These results improve the existing limits by almost three orders of magnitude (four in the case of 0ν mode).